Density profile of multi-state fuzzy dark matter

TL;DR

This paper derives a density profile for multi-state fuzzy dark matter by solving equations of motion with the WKB approximation, revealing a finite energy gap and a profile similar to the Burkert profile.

Contribution

It introduces a novel approach to modeling fuzzy dark matter density profiles considering excited states and a finite energy gap.

Findings

Density profile similar to Burkert profile

Finite energy gap in excited states spectrum

Potential creation of the gap via decay processes

Abstract

Equations of motion for excited states of weakly self-interacting bosons forming fuzzy dark matter are solved using the WKB approximation. The contribution of self-interactions are neglected in the equations of motion. Wave functions of excited states are expressed in terms of a yet undetermined gravitational potential. At equilibrium, the contributions of states to the density distribution are summed using Bose-Einstein statistics. Combined with the Poisson equation, a differential equation is obtained for the gravitational potential, which has physically acceptable solutions only if the energy spectrum of excited states has a finite gap, corresponding to a finite virial radius. Such a gap could be created by decay processes, in first order perturbation of the self-interaction potential. The obtained density profile is found to be similar to the Burkert profile.